If Joel did serve in the 6th Louisiana Cavalry, it stands to reason you cannot find records of his service as there are no surviving muster rolls for his Company E which survived to be recorded in the Compiled Service Records. There are only a handful of Company E members who have records, but these were derived from Federal POW/surrender and Officer’s supply requisitions.

As to your statement “I am assuming since she got the pension he died as a result of injury or illness from the war.” No, pensions were provided for those who honorably served and were at the time of filing, indigent. See,

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On April 2, 1891, with the passage of Act 91, "An act for the relief of certain soldiers of the late War Between the States" Arkansas became one of the first Southern states to grant annual pensions to its resident ex-Confederate servicemen and their widows. By common consent, Arkansas and the other former Confederate states agreed that pensions for C.S.A. service would be granted by the state in which the veteran or his widow lived at the time of application rather than by the state from which he served. Act 91 created a State Board of Pensions composed of the governor, the attorney general, and the auditor of state. Seventy-five local pension boards, one in each county, were created at the same time. Each was composed of the county judge, the sheriff, and the county clerk. These boards oversaw the granting of pensions. Some 45,000 veterans and widows of veterans received benefits under the provisions of this Act until the creation of the State Department of Public Welfare in 1939. After that date pensions were administered by that agency.

Initially, only needy, indigent or disabled veterans, who had been honorably discharged or unmarried needy or indigent widows of veterans, were eligible for pensions. Beginning in 1915 needy widows who had not remarried, and who were born before 1878 and widowed mothers of veterans were added to those who could file for benefits. However, few veterans' mothers remained alive to apply. That year a definition of indigence as someone owning less than $500 worth of real estate or having an annual income of less than $250, was added to the law. In 1937 widows who had married veterans before 1927 became eligible. However, in 1939 a provision was added that applicants had to be born before 1870. Upon a veteran's death, his widow automatically became eligible for his pension. During the 1920s and 1930s, the Arkansas General Assembly regularly added individual veterans or widows to the pension rolls without regard to their qualifications. In many cases, these pensioners do not have files.

From 1891 until 1915 the annual payment per pension was $25.00. After that date, the amount was raised to $100.00 per year. Inadequate funding prevented most pensioners from getting their full yearly payment. Applications had to be submitted to the county boards before July 1 each year. After review and approval by the state board, payments in the form of State Treasury Warrants were mailed out once a year after September 1. However, the individual pensioners did not receive the warrants. They were mailed to and distributed by the county board.

A typical pension file contains an application form signed by the veteran or his widow, a doctor's certificate of disability, and a statement of indigence. The file also usually contains two affidavits from "comrades at arms" attesting to the veteran's military service. A widow's application usually contains information on her husband's death.

http://www.ark-ives.com/documenting/confed_pensions.aspx

Were their any soldiers who attested to his service in her pension application?

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"The exact date and place of organization of this regiment remain a mystery. Several companies were added to Lieutenant Colonel William Harrison's Cavalry Battalion, possibly as late as January, 1865, to make it a regiment. Some records indicate that the regiment existed as early as September, 1864. Whatever the case may be, the regiment saw little, if any, fighting during the war. Most of its service consisted of courier and guard duty around Shreveport and Alexandria. Individual companies of the regiment may have conducted independent campaigns against deserters, draft dodgers, and Jayhawkers in northern and western Louisiana. At various times, Harrison's regiment composed part of the cavalry brigades commanded by Colonel William G. Vincent and Colonel Isaac F. Harrison. Toward the end of the war, the regiment was dismounted and attached to an infantry brigade. The regiment appears to have disbanded with other units near Mansfield in May, 1865."
http://www.acadiansingray.com/6th%20Regt.%20Cav.htm